Model-based RL in Contextual Decision Processes: PAC bounds and Exponential Improvements over Model-free Approaches
This work addresses the problem of efficient exploration in reinforcement learning for researchers and practitioners, demonstrating a significant theoretical separation between model-based and model-free methods in rich-observation environments.
The paper tackles the sample complexity of model-based reinforcement learning in contextual decision processes by introducing algorithms with sample complexity governed by a new structural parameter called witness rank, which is shown to be smaller than existing model-free parameters and leads to exponential improvements in settings like factored MDPs.
We study the sample complexity of model-based reinforcement learning (henceforth RL) in general contextual decision processes that require strategic exploration to find a near-optimal policy. We design new algorithms for RL with a generic model class and analyze their statistical properties. Our algorithms have sample complexity governed by a new structural parameter called the witness rank, which we show to be small in several settings of interest, including factored MDPs. We also show that the witness rank is never larger than the recently proposed Bellman rank parameter governing the sample complexity of the model-free algorithm OLIVE (Jiang et al., 2017), the only other provably sample-efficient algorithm for global exploration at this level of generality. Focusing on the special case of factored MDPs, we prove an exponential lower bound for a general class of model-free approaches, including OLIVE, which, when combined with our algorithmic results, demonstrates exponential separation between model-based and model-free RL in some rich-observation settings.